Generalized multivariate exponential power prior for wavelet-based multichannel image restoration

2013 ◽  
Author(s):  
Y. Marnissi ◽  
A. Benazza-Benyahia ◽  
E. Chouzenoux ◽  
J.-C. Pesquet
Keyword(s):  
Image Restoration ◽  
Power Prior ◽  
Exponential Power ◽  
Multivariate Exponential

scholarly journals Some Properties of Univariate and Multivariate Exponential Power Distributions and Related Topics

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1918
Author(s):  
Victor Korolev
Keyword(s):  
Limit Theorems ◽  
Random Sums ◽  
Random Vectors ◽  
Asymptotic Results ◽  
Space Of Distributions ◽  
Gamma Distributions ◽  
Statistical Regularities ◽  
Exponential Power ◽  
The One ◽  
Multivariate Exponential

In the paper, a survey of the main results concerning univariate and multivariate exponential power (EP) distributions is given, with main attention paid to mixture representations of these laws. The properties of mixing distributions are considered and some asymptotic results based on mixture representations for EP and related distributions are proved. Unlike the conventional analytical approach, here the presentation follows the lines of a kind of arithmetical approach in the space of random variables or vectors. Here the operation of scale mixing in the space of distributions is replaced with the operation of multiplication in the space of random vectors/variables under the assumption that the multipliers are independent. By doing so, the reasoning becomes much simpler, the proofs become shorter and some general features of the distributions under consideration become more vivid. The first part of the paper concerns the univariate case. Some known results are discussed and simple alternative proofs for some of them are presented as well as several new results concerning both EP distributions and some related topics including an extension of Gleser’s theorem on representability of the gamma distribution as a mixture of exponential laws and limit theorems on convergence of the distributions of maximum and minimum random sums to one-sided EP distributions and convergence of the distributions of extreme order statistics in samples with random sizes to the one-sided EP and gamma distributions. The results obtained here open the way to deal with natural multivariate analogs of EP distributions. In the second part of the paper, we discuss the conventionally defined multivariate EP distributions and introduce the notion of projective EP (PEP) distributions. The properties of multivariate EP and PEP distributions are considered as well as limit theorems establishing the conditions for the convergence of multivariate statistics constructed from samples with random sizes (including random sums of random vectors) to multivariate elliptically contoured EP and projective EP laws. The results obtained here give additional theoretical grounds for the applicability of EP and PEP distributions as asymptotic approximations for the statistical regularities observed in data in many fields.

Analysis of 3-d molecular distribution with the digital imaging microscope

1988 ◽  
Vol 46 ◽  
pp. 40-41
Author(s):  
W.A. Carrington ◽  
F.S. Fay ◽  
K.E. Fogarty ◽  
L. Lifshitz
Keyword(s):  
Image Restoration ◽  
Digital Imaging ◽  
Fluorescent Dyes ◽  
Optical Axis ◽  
Computer Hardware ◽  
Computer Algorithms ◽  
Low Contrast ◽  
Specific Proteins ◽  
Effective Use ◽  
Single Living Cells

Advances in digital imaging microscopy and in the synthesis of fluorescent dyes allow the determination of 3D distribution of specific proteins, ions, GNA or DNA in single living cells. Effective use of this technology requires a combination of optical and computer hardware and software for image restoration, feature extraction and computer graphics.The digital imaging microscope consists of a conventional epifluorescence microscope with computer controlled focus, excitation and emission wavelength and duration of excitation. Images are recorded with a cooled (-80°C) CCD. 3D images are obtained as a series of optical sections at .25 - .5 μm intervals.A conventional microscope has substantial blurring along its optical axis. Out of focus contributions to a single optical section cause low contrast and flare; details are poorly resolved along the optical axis. We have developed new computer algorithms for reversing these distortions. These image restoration techniques and scanning confocal microscopes yield significantly better images; the results from the two are comparable.

Improving x-ray map resolution with image restoration techniques

1996 ◽  
Vol 54 ◽  
pp. 598-599
Author(s):  
Richard B. Mott ◽  
John J. Friel ◽  
Charles G. Waldman
Keyword(s):  
Image Restoration ◽  
Hubble Space Telescope ◽  
Extensive Literature ◽  
Small Object ◽  
X Rays ◽  
X Ray ◽  
Mapping Parameters ◽  
The Matrix ◽  
The 1960S ◽  
Map Resolution

X-rays are emitted from a relatively large volume in bulk samples, limiting the smallest features which are visible in X-ray maps. Beam spreading also hampers attempts to make geometric measurements of features based on their boundaries in X-ray maps. This has prompted recent interest in using low voltages, and consequently mapping L or M lines, in order to minimize the blurring of the maps.An alternative strategy draws on the extensive work in image restoration (deblurring) developed in space science and astronomy since the 1960s. A recent example is the restoration of images from the Hubble Space Telescope prior to its new optics. Extensive literature exists on the theory of image restoration. The simplest case and its correspondence with X-ray mapping parameters is shown in Figures 1 and 2.Using pixels much smaller than the X-ray volume, a small object of differing composition from the matrix generates a broad, low response. This shape corresponds to the point spread function (PSF). The observed X-ray map can be modeled as an “ideal” map, with an X-ray volume of zero, convolved with the PSF. Figure 2a shows the 1-dimensional case of a line profile across a thin layer. Figure 2b shows an idealized noise-free profile which is then convolved with the PSF to give the blurred profile of Figure 2c.

Maximum image restoration in nuclear medicine

1990 ◽  
Vol 137 (3) ◽  
pp. 163 ◽  
Author(s):  
V.A. Oliveira ◽  
J.M. Nightingale
Keyword(s):  
Nuclear Medicine ◽  
Image Restoration

CNN-based Classification of Degraded Images

2020 ◽  
Vol 2020 (10) ◽  
pp. 28-1-28-7 ◽  
Author(s):  
Kazuki Endo ◽  
Masayuki Tanaka ◽  
Masatoshi Okutomi
Keyword(s):  
Neural Networks ◽  
Image Restoration ◽  
Image Classification ◽  
Convolutional Neural Networks ◽  
Deep Convolutional Neural Networks ◽  
Alternative Approach ◽  
Degraded Image ◽  
Degraded Images ◽  
Straightforward Approach

Classification of degraded images is very important in practice because images are usually degraded by compression, noise, blurring, etc. Nevertheless, most of the research in image classification only focuses on clean images without any degradation. Some papers have already proposed deep convolutional neural networks composed of an image restoration network and a classification network to classify degraded images. This paper proposes an alternative approach in which we use a degraded image and an additional degradation parameter for classification. The proposed classification network has two inputs which are the degraded image and the degradation parameter. The estimation network of degradation parameters is also incorporated if degradation parameters of degraded images are unknown. The experimental results showed that the proposed method outperforms a straightforward approach where the classification network is trained with degraded images only.

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